see, for example, Section I.4.2 in [1]} for  such an extension. In addition, from (REF ) and the estimate
\(\Vert V;L^2(\varpi ^0 \cap \lbrace \vert x_1 \vert <\varepsilon \rbrace )\Vert ^2 \le C\varepsilon \Vert V;H^1(\varpi ^0 )\Vert ^2\quad \forall V\in H^1(\varpi ^0)\) 
